Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

If $ab c = m$ and $det P = a c b b a c c b a$ , where $P$ is an orthogonal matrix.

The cubic equation whose roots are $a^{- 1}, b^{- 1}$ and $c^{- 1}$ can be

Options:

Answer:

Solution:

We know the cubic equation whose roots are $α, β, γ t^{3} - (α + β + γ) t^{2} + (α β + β γ + α γ) + α β γ = 0$ , where t is origin. The equation whose roots are $a^{- 1}, b^{- 1}, c^{- 1}$ is $t^{3} - (\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) t^{2} + (\frac{1}{ab} + \frac{1}{b c} + \frac{1}{c a}) t + \frac{1}{ab c} = 0$ $\Rightarrow t^{3} - (0) t^{2} + (\frac{\pm 1}{n}) t + \frac{1}{m} = 0 \Rightarrow m t^{3} \pm t + 1 = 0$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...